On a matrix group constructed from an {R, s +1, k}-potent matrix

摘要

Let R∈C~(n×n) be a {k}-involutory matrix (that is, R~k=I_n) for some integer k≥2, and let sbe a nonnegative integer. A matrix A ∈ C~(n×n) is called an {R, s +1, k}-potent matrix if A satisfies RA =A~(s+1)R. In this paper, a matrix group corresponding to a fixed {R, s +1, k}-potent matrix is explicitly constructed, and properties of this group are derived and investigated. This group is then reconciled with the classical matrix group G_A that is associated with a generalized group invertible matrix A.